The Paradox machine was a type of technology that was capable of creating a tear in space and time.
The Master used such a machine by cannibalising the The Doctor's TARDIS in order to allow his army of Toclafane to invade Earth. The device created a tear in the sky allowing millions of the sphere-like aliens to attack the planet and its populace. (DW: The Sound of Drums)
The device was designed to prevent a time paradox would occur. As the Toclafane Human were Humanity from the future, their attacks on their ancestors meant that, normally, they were destroying themselves and thus should have been erased from history. However, the use of the paradox machine prevented such an outcome from happening allowing the Toclafane to continue their enslavement of their ancestors. The device was destroyed by Captain Jack Harkness. (DW: The Last of the Time Lords)
